PHYSICAL REVIEW B
VOLUME 57, NUMBER 1
1 JANUARY 1998-I
Current-induced resistivity switching effects near the melting line in detwinned YBa2Cu3O72d
S. N. Gordeev,* D. Bracanovic, A. P. Rassau, and P. A. J. de Groot
Department of Physics, University of Southampton, Southampton, SO17 1BJ, United Kingdom
R. Gagnon and L. Taillefer
Department of Physics, McGill University, Montreal (Quebec), Canada H3A 2T8
~Received 22 September 1997!
Hysteresis of the E-J characteristics has been observed in the vicinity of the melting line using a sensitive
superconducting quantum interference device picovoltmeter with millikelvin temperature resolution. It was
found that in this region the system could be switched from a lower- to a higher-resistivity state by applying
a current in excess of a threshold value. From the comparison of transport and ac susceptibility data, we
conclude that in this hysteretic region the vortex solid and liquid phases coexist and that the observed transport
phenomena can be explained in terms of the rearrangement of solidified vortex domains.
@S0163-1829~98!07201-4#
Recent calorimetric1 and magnetization2 studies have unambiguously shown that, in clean YBa2Cu3O72d crystals, the
phase transition from the vortex liquid to the vortex solid
state is first order. In transport measurements this transition
is seen as a sharp drop in the tail of both the temperature and
field dependences of the resistivity together with associated
hysteresis.3–7 Safar et al.3 have attributed this hysteresis to
the supercooling and superheating effects which normally
accompany a first-order phase transition. Charalambous
et al.6 found that changes in the probing current only had an
effect on the r (T) curves obtained on heating and not those
obtained on cooling, thereby concluding that the vortex system can be superheated, but not supercooled. More recently,
computer simulations by Dominguez et al.8 have indicated
that a sufficiently large transport current could induce melting of the vortex lattice.
To investigate the effect of the probing currents close to
the melting line, we have performed a detailed study of the
E-J curves in addition to more conventional r (T) measurements. We explicitly demonstrate that the E-J curves in this
region show hysteretic ‘‘switching’’ behavior. From a comparative study of r (T) and x 8 (T), we conclude that the vortices in the hysteretic region are not in a single state, rather
that in this region, vortex liquid and solid phases coexist. We
have also observed that a current density, in excess of some
threshold value, can switch the vortex system from the
branch of the resistivity hysteresis curve obtained on heating
to that obtained on cooling. We interpret this observation in
terms of current-induced melting of superheated regions of
the vortex solid.
Our experiments were performed on an YBa2Cu3O72d
single crystal ~of dimensions 1.1 mm30.35 mm365 mm!,
grown in an Y-stabilized ZrO2 crucible and detwinned as
described elsewhere.9 A superconducting quantum interference device ~SQUID! picovoltmeter was used to perform
magnetoresistance measurements using a conventional fourprobe technique ~with H i c!. The probing current (J i a) was
modulated with a single-polarity square wave of frequency
f m 568 Hz. Resistivity versus temperature hysteresis loops
were obtained by warming and cooling the sample at a con-
stant rate of 0.01 K/min. During E-J measurements, the temperature stability was ;1 mK. ac susceptibility measurements were performed using a coaxial mutual inductance
system with superimposed ac and dc fields.10
For J50.44 A/cm2 the sample under investigation exhibited Ohmic r (T) behavior very similar to that observed in
previous experiments.3,4 The resistivity below the melting
line dropped to zero over very narrow temperature interval
(,0.03 K), and the r (T) dependence was found to be hysteretic in this vicinity ~see Fig. 1!. Notice in particular that,
as is usually observed,3–7 the hysteresis loop was asymmetric: The curve obtained on warming was smoother than
that obtained on cooling. For current densities less than a
threshold value J t 50.6 A/cm2, the shape of the r (T) curves
and the width of the hysteresis were independent of the current density.
Figure 2 presents a set of isothermal E-J curves for B
52 T. The ‘‘cooled-state’’ curves ~lines! were obtained by
cooling from the vortex liquid state with subsequent curves
separated by a temperature step DT55 mK. Each separate
curve was obtained by sweeping the current density from 0
to 10 A/cm2. The symbols represent the E-J curves for a
0163-1829/98/57~1!/645~4!/$15.00
645
57
FIG. 1. Temperature dependence of the normalized resistivity at
B52 T, showing the hysteresis around T m .
© 1998 The American Physical Society
646
S. N. GORDEEV et al.
FIG. 2. E-J characteristics in the vicinity of T m . The lines
represent the E-J curves of the cooled state for temperatures in the
range 88.955–89.015 K separated by 5-mK steps. The symbols
show the E-J curves for the heated state at T588.995 K for four
successive runs. Each separate curve was obtained by sweeping the
current density from zero up to a progressively higher maximum
value J max : ~d! 0.5 A/cm2, ~3! 0.75 A/cm2, ~s! 1.0 A/cm2, and
~1! 1.5 A/cm2.
‘‘heated state’’ obtained by warming the sample from 88 K
~where the vortex system is in the solid state! up to 88.995
K. This state was then investigated by probing the E-J dependences in the regime of increasing J for four successive
runs such that each subsequent run reached a higher maximum current density J max . It can be seen from Fig. 2 that
provided J did not exceed a threshold value J t
('0.6 A/cm2), the heated state was stable with a reproducible E-J dependence located well below the cooled-state
curve for the same temperature (T588.995 K). The shift
between these states corresponds to a temperature difference
;8 mK, which is in agreement with the width of the r (T)
hysteresis ~as shown in Fig. 1!.
However, if the current during a particular run exceeded
J t , then subsequent runs demonstrated a higher Ohmic resistivity r l 5E/J at low currents. The higher the probing current density, the larger was the r l value. For J.2J t saturation occurred, after which the E-J curve reproduced the
shape of the cooled-state curve at the same temperature, but
with a small vertical shift. This shift can be explained in
terms of the temperature reproducibility of our system,
which is ;2 mK for 1-K temperature cycles. It is therefore
clear that a sufficiently large current density can switch the
vortex system from a low-resistivity heated state to a highresistivity cooled state.11
As shown in Fig. 3, similar ‘‘switching’’ behavior was
observed when the heated state was prepared by sweeping B
at constant T. The solid lines show the E-J curves for the
cooled state at B53 T. A heated state was obtained by
sweeping the magnetic field from 3.0 to 2.5 T and then back
to 3 T ~with T587.33 K!. This state was probed by increasing the current density J from 0 to 10 A/cm2 ~solid circles!.
A subsequent current sweep ~open circles! coincided closely
with the cooled-state curve for the same temperature. This
demonstrates once more the switching effect displayed in
Fig. 2. A cooled state was prepared by increasing B up to 3.5
57
FIG. 3. Demonstrates the effect of probing current on the E-J
curves for B53 T. The solid lines show cooled-state E-J curves for
temperatures in the range 87.29–87.36 K separated by 5-mK steps.
The circles show two successive runs for the heated state at T
587.330 K @~d! first run, ~s! second run#. The crosses show two
successive runs for the cooled state at T587.335 K @~1! first run,
~3! second run#.
T and dropping back to 3 T ~with T587.335 K!. The stability of this state is demonstrated by the similarity of the E-J
curves for two successive current sweeps ~vertical and diagonal crosses!.
Jiang et al.7 have proposed the following explanation for
the r (T) hysteresis observed in the vicinity of the melting
line. On cooling the vortex system, just below T m a finite
shear modulus develops, but initially this is insufficient to
impede the motion of the vortices. The system will therefore
supercool until the shear elastic energy exceeds the work
done by the transport current. In contrast, when the sample is
warmed up starting from the vortex solid state, initially the
vortex velocities are lower. This means that less work is
done by the transport current Lorentz force, and thus the
vortex lattice should remain intact to higher temperatures.
Our experiments demonstrate that the resistivity hysteresis shown in Fig. 1 is not due to the mechanism proposed by
Jiang et al.7 Measurements were performed using a singlepolarity square-wave current, and thus for half of each modulation period the current flowing through the sample was
zero. During these half-periods, the work done by the current
was also zero. It follows that at temperatures for which the
shear modulus is finite the vortex system should freeze.
Thus, for this particular case, there should be no difference
between the transition temperature obtained on heating and
that obtained on cooling according to the mechanism proposed by Jiang et al.
Figure 4 compares the resistivity r (T) and the real part of
the ac susceptibility x 8 (T) in the vicinity of the melting line
~at B52 T!. From this it can be seen that the vortex-liquid–
to–solid transition manifests itself as a simultaneous sharp
change in both r (T) and x 8 (T) dependences. Notice that in
contrast to x 8 (T) measurements performed on less clean
samples ~which do not show a first-order melting transition!,
we have observed a well-defined linear drop in x 8 (T). 10 The
temperature width of the linear region (DT tr50.35 K) was
independent of the applied ac field and therefore on the magnitude of the induced currents. These results are strikingly
57
CURRENT-INDUCED RESISTIVITY SWITCHING . . .
FIG. 4. Comparison of the temperature dependence of the resistivity ~for J50.44 A/cm2! and ac susceptibility ~for ac fields of 50
and 25 mT! at B52 T. All of the curves were obtained in the
regime of increasing temperature. The dashed lines delimit the transition region where the liquid and solid phases coexist. The dotted
lines drawn along the ac susceptibility curves in the transition region are a guide to the eye.
similar to those recently obtained by Fendrich et al.12 In a
comparative study of transport and magnetic properties, they
found that the onset of the resistivity and magnetization transitions coincided closely and that the reversible dc magnetization showed a sharp linear increase over a temperature
interval ;0.2 K. They associated this rise with an increase in
the fraction of the solid phase. Thus transport phenomena
within this region can be understood in terms of coexistent
vortex solid and liquid phases. Furthermore, they deduced
from their results that the Ohmic resistivity dropped to zero
where the fraction of solid phase reached 20% and explained
this in terms of percolative processes.13
While ac susceptibility measurements do not reflect equilibrium ~thermodynamic! quantities, there is compelling evidence to suggest that the linear sections of the x 8 (T) dependences can be identified with the temperature region over
which the liquid and solid vortex phases coexist. Of great
significance is the fact that the linear region of the x 8 (T)
dependences shows a remarkable correspondence, both in
shape and position, to the transition region as observed by
Fendrich et al. in dc magnetization measurements. Moreover, the ac susceptibility transitions are very well defined
with onsets which coincide closely with the start of the resistivity transition for the same sample.
The S-shaped E-J curves shown in Fig. 2 can also be
explained in terms of coexistent vortex liquid and solid
phases. In the low-current region of the curves, the response
is Ohmic, suggesting that at this limit the dissipative contribution due to thermally activated motion of the vortex solid
is negligible.14 Thus the implication is that the low-current
Ohmic part of the E-J curves is controlled by vortex liquid
flowing in channels between static solid domains. As T decreases, these domains grow and as a result the Ohmic resistivity is observed to fall. This resistivity finally drops to zero
upon closing of the last channel between domains.15
At high currents the E-J curves are again Ohmic, but with
a much higher resistivity r ff due to Bardeen-Stephen free
flux flow of practically all the vortices.5 In the region of
647
intermediate current densities, the E-J curves show strong
upward curvature. As seen from Fig. 2, the transition from
Ohmic to non-Ohmic behavior at low currents is not a
smooth crossover as would be the case for a transition from
thermally assisted flux flow ~TAFF! to a flux creep regime.
Instead, the nonlinear regime starts at a well-defined crossover current density J cr ~0.7 A/cm2 for T589.995 K!. We
suggest that this crossover marks the point at which the vortices within the solid domains start to move.
The central result of our paper is as follows. We have
found that the threshold density J t , at which current begins
to affect the ‘‘heated state,’’ almost coincides with J cr at
which the E-J curve ~for the same temperature! deviates
from Ohmic behavior ~see Fig. 2!. This implies that both
effects are consequences of the same dynamic process. Thus
the threshold current for the ‘‘switching’’ effect also marks
the point at which the vortex-solid domains start to move.
Our understanding of the current-induced switching effect is
based on the assumption that the local melting temperature
varies throughout the sample. This is supported by our ac
susceptibility data,10 which showed that the width of the
melting transition region (DT tr), where the vortex liquid and
solid phases coexist, varied between 0.35 and 0.55 K depending on the particular sample. This implies that factors
such as sample inhomogeneity lead to a variation of the local
melting temperature within a given sample. Thus, as the
melting line is approached from the direction of the vortex
solid, domains of solidified vortices will persist at points
where the local melting temperature T Lm is highest. The eventual result will be a number of isolated domains surrounded
by channels of free flux flow.
It is expected that in the heated state there will be regions
within solid or possibly whole domains which are superheated relative to the temperature of the region in which they
are located.3–5 We propose that under the influence of transport current Lorentz forces ~for J.J cr! the solid domains
will be displaced into regions where T Lm is lower, leading to
partial or complete melting. Resolidification is expected to
take place at the peaks in the melting temperature profile, but
not at points which were originally occupied by superheated
solid. Thus, on considering the properties of the low-current
Ohmic state, the net result will be a reduction in the fraction
of vortices in the solid phase. This accounts for the order of
magnitude difference between the dissipation in the original
low-current state and the state obtained upon switching ~see
Fig. 2!. It is also clear from this explanation why a transport
current causes switching from the heated state to the cooled
state, but not vice versa: A transport current can induce melting, but not solidification. Recent numerical simulations by
Dominguez et al.8 have suggested that sufficiently large currents, much larger than the depinning current, should induce
melting due to the blowing out of thermally induced vortex
loops. It is, however, clear from our experiments that there is
an additional distinct mechanism of current-induced melting.
We have seen that this mechanism becomes effective at
much lower currents.
Using the model of coexistent phases, we can now explain
the observed r (T) behavior in the vicinity of T m . For J
,J cr the current is insufficient to move the solid domains,
resulting in current-independent resistivity hysteresis. For J
.J cr a switching effect occurs and the resistivity depen-
648
S. N. GORDEEV et al.
dences of the heating and cooling cycles collapse into a
single r (T) curve. In addition, our interpretation also explains the lack of time dependence observed by Jiang et al.7
in their r (T) measurements. In the hysteretic region energy
dissipation is largely due to the flow of vortex liquid between
solid domains. Thus the system should not evolve with time
~as would be expected for a ‘‘glassy’’ solid phase16!.
In conclusion we have demonstrated, from the analysis of
E-J curves in the r (T) hysteretic region, that a sufficiently
large probing current density ~J.1.5 A/cm2 for B52 T! can
switch the vortex system from a lower-resistivity state obtained on heating into a higher-resistivity state. This higherresistivity state was shown to be the same as the state obtained on cooling from the vortex liquid state. The switching
*On leave from the Moscow Institute of Radioengineering, Electronics and Automation, 117454 Moscow, Russia.
1
A. Schilling, R. A. Fisher, N. E. Phillips, U. Welp, D. Dasgupta,
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3
H. Safar, P. L. Gammel, D. A. Huse, D. J. Bishop, W. C. Lee, J.
Giapintzakis, and D. M. Ginsberg, Phys. Rev. Lett. 69, 824
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5
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6
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7
W. Jiang, N-C. Yeh, D. S. Reed, U. Kriplani, and F. Holtzberg,
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8
D. Dominguez, N. Gro” nbech-Jensen, and A. R. Bishop, Phys.
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57
effect was explained within the framework of a model of
coexistent phases, as supported by our ac susceptibility results. According to this explanation, the probing current
moved solidified vortices to regions where the local melting
temperature was lower, thereby inducing melting of superheated sections of the vortex solid.
This project is supported by the EPSRC ~UK!. We appreciate helpful discussions with M. Oussena and are grateful to
V. B. Geshkenbein, A. A. Zhukov, M. Charalambous, and
M. V. Indenbom for useful comments. D.B. acknowledges
funding from the University of Southampton. R.G. and L.T.
acknowledge funding from NSERC ~Canada!, FCAR of
Quebec, and CIAR ~Canada!. L.T. acknowledges the support
of the Sloan Foundation.
9
R. Gagnon, C. Lupien, and L. Taillefer, Phys. Rev. B 50, 3458
~1994!.
10
D. Bracanovic, S. N. Gordeev, S. Pinfold, R. Langan, M. Oussena, and P. A. J. de Groot, Physica C ~to be published!.
11
In principle, such effects could be induced by Joule heating in the
sample contacts. However, since Joule heating is proportional to
J 2 , the resultant temperature increase should lead to a pronounced bending of all the E-J curves, contrary to what we
have observed.
12
J. Fendrich, U. Welp, W. K. Kwok, A. E. Koshelev, G. W. Crabtree, and B. W. Veal, Phys. Rev. Lett. 77, 2073 ~1996!.
13
G. Deutscher, in Percolation, Localisation and Superconductivity,
Vol. B109 of NATO Advanced Study Institute, Series B: Physics,
edited by A. M. Goldman and S. A. Wolf ~Plenum, New York,
1984!, p. 94.
14
If there were a significant contribution to the dissipation due to
the motion of the vortex solid, then we would expect the response to be highly nonohmic. This can be clearly seen from the
response at higher currents for which there is definitely dissipation due to the motion of both vortex solid and liquid.
15
In the mixed-state regime, the flow of current is expected to be
highly nonuniform, and thus within this region the current density J reflects the average value across the whole cross section
of the sample rather than the value in any particular region.
16
V. B. Geshkenbein, L. B. Ioffe, and A. I. Larkin, Phys. Rev. B 48,
9917 ~1993!.